What the average, or arithmetic mean, is
In everyday speech and in most maths classes, "the average" means the arithmetic mean: add the numbers together and divide by how many there are. It is a single number that stands in for a whole list, so it is the first summary people reach for when they compare test scores, prices, times or measurements. This calculator takes 1 to 500 numbers, shows the sum, the count and the mean with the steps written out, and also reports the smallest and largest value so you can see the spread at a glance.
Sum divided by count: a worked example
For the numbers 2, 7, 19, 24 and 25 the sum is 77 and the count is 5, so the mean is 77 ÷ 5 = 15.4. The mean does not have to be one of the numbers in the list, and it does not have to be a whole number. It always lies between the smallest value (2) and the largest (25), and the values below it balance the values above it, which is why a number line with a marker at the mean is a useful picture.
Pasting numbers from a spreadsheet
You can type numbers separated by commas, or copy a column or a block of cells from a spreadsheet and paste it straight in. Commas, spaces, tabs and line breaks all count as separators, so a mix such as "1 [tab] 2 [new line] 3 4,5" is read as 5 values. Use a dot for the decimal point and leave out thousands separators. A decimal comma is a separator here: "3,5" is read as the two numbers 3 and 5, not as 3.5, so write 3.5 if you mean three and a half. The page lists every value it read, and if an entry is not a number, such as a stray letter, it names that entry and stops instead of quietly skipping it. That is deliberate: a silently dropped value changes the mean without telling you.
How one value moves the mean
The mean is sensitive to extreme values. Take 12, 14, 15, 16, 18 and 95. Their mean is 28.3333333333, which is higher than five of the six numbers, because 95 pulls it up. Leave 95 out and the mean of the other five is 15, a change of -13.3333333333. The leave-one-out control on this page does exactly that: pick any row and the calculator shows the mean without it, the change from the full mean and the new sum, without altering your list. Try it on the first example: leaving out 25 changes the mean from 15.4 to 13, a change of -2.4.
If a list contains an outlier, the median (the middle value when the numbers are sorted) can describe the typical value better. In the list above the middle two numbers are 15 and 16, so the median is 15.5, close to the mean of the five values that remain after leaving out 95. This page reports the mean, sum, count, smallest and largest values only, so use it alongside your own judgement about whether an outlier is a real observation or a data-entry slip.
Zero, negative and decimal values
The calculator accepts positive and negative numbers and decimals. The values -1 and 1 have a sum of 0 and a mean of 0. The list -1.5, 2.25 and 4 has a sum of 4.75, and its mean, about 1.5833333333, is shown rounded to ten decimal places and marked as approximate because it does not end. A list with a single number has that number as its mean (42), and the leave-one-out control is switched off because nothing would be left.
Why the arithmetic is exact
Computers store most decimals in binary, which cannot represent numbers such as 0.1 exactly, so ordinary floating-point sums can show tiny errors like 0.30000000000000004. This calculator reads your numbers as exact decimals, adds them with whole-number arithmetic and rounds only when it displays the answer, so 0.1, 0.2 and 0.3 add to 0.6 and average exactly 0.2. Each number can have up to 20 digits and up to 10 decimal places.
When a simple average is not the right tool
A plain mean treats every value equally. If your values should count for different amounts, as with course grades that have different weights, use the weighted grade calculator. If the numbers are yearly investment returns, the simple mean of the percentages can overstate what an investor actually earned, so use the average return calculator, which compares arithmetic and compound figures. An average of group averages is also only correct when the groups are the same size. When you want to know how many survey responses you need before an average is trustworthy, see the sample size calculator, and for the spread of a bell-shaped distribution use the normal distribution calculator.
Average calculator questions
How do I calculate the average of a list of numbers?
Add all the numbers and divide by how many there are. For 2, 7, 19, 24 and 25 the sum is 77, the count is 5 and the average is 15.4.
Is the average the same as the mean?
In most school and everyday use, yes: "average" means the arithmetic mean. Statisticians also use the word for the median and the mode, which are different measures, so say which one you mean when it matters.
How does removing one number change the average?
The new mean is the sum of the other numbers divided by one fewer. Removing a value above the mean lowers the mean, and removing a value below it raises it. Use the leave-one-out control to see the exact change for any row.
Can I paste numbers from Excel or Google Sheets?
Yes. Copy a column or a range of cells and paste it into the box. Tabs and line breaks are treated as separators. Because blank cells and text cells could hide a mistake, the calculator tells you about empty entries and stops on any entry that is not a number.
Can the average be negative or zero?
Yes. If the negative numbers outweigh the positive ones the mean is negative, and a list such as -1 and 1 has a mean of 0.
How many numbers can I enter?
From 1 up to 500 numbers. A list longer than that is refused with a clear message rather than being cut off.